Question

An ellipse is centered at the origin. Find it’s equation.

Answer 1

Answer:

(x)^2        (y)^2

---------- + --------- = 1

 4              3

Step-by-step explanation:

The standard equation for an ellipse is

(x-h)^2     (y-k)^2

---------- + --------- = 1

a^2            b^2

The center is at (h,k)

The vertices are at (h±a, k)

The foci are at (h±c,k )

Where c is sqrt(a^2 - b^2)

It is centered at the origin so h,k are zero

(x)^2        (y)^2

---------- + --------- = 1

a^2            b^2

The center is at (0,0)

The vertices are at (0±a, 0)

The foci are at (0±c,0 )

The vertices are (±2,0)  so a =2

The foci is 1

c = sqrt(a^2 - b^2)

1 = sqrt(2^2 - b^2)

Square each side

1 = 4-b^2

Subtract 4 from each side

1-4 = -b^2

-3 = -b^2

3= b^2

Take the square root

b=sqrt(3)

(x)^2        (y)^2

---------- + --------- = 1

 4              3